Actually, no, it shouldn't.
What the Twenty-First Amendment primarily does is to repeal the Eighteenth Amendment. This doesn't mean that the federal government cannot ban alcohol, just that the one ban that was put into place by the Eighteenth Amendment is no longer in effect.
It also certainly does nothing to prevent states or lower governments from banning or restricting alcohol; and in fact, it strengthens their power to do so.
Section 1. The eighteenth article of amendment to the Constitution of the United States is hereby repealed.
Section 2. The transportation or importation into any State, Territory, or possession of the United States for delivery or use therein of intoxicating liquors, in violation of the laws thereof, is hereby prohibited.
Section 3. This article shall be inoperative unless it shall have been ratified as an amendment to the Constitution by conventions in the several States, as provided in the Constitution, within seven years from the date of the submission hereof to the States by the Congress.